137537is an odd number,as it is not divisible by 2
The factors for 137537 are all the numbers between -137537 and 137537 , which divide 137537 without leaving any remainder. Since 137537 divided by -137537 is an integer, -137537 is a factor of 137537 .
Since 137537 divided by -137537 is a whole number, -137537 is a factor of 137537
Since 137537 divided by -1 is a whole number, -1 is a factor of 137537
Since 137537 divided by 1 is a whole number, 1 is a factor of 137537
Multiples of 137537 are all integers divisible by 137537 , i.e. the remainder of the full division by 137537 is zero. There are infinite multiples of 137537. The smallest multiples of 137537 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 137537 since 0 × 137537 = 0
137537 : in fact, 137537 is a multiple of itself, since 137537 is divisible by 137537 (it was 137537 / 137537 = 1, so the rest of this division is zero)
275074: in fact, 275074 = 137537 × 2
412611: in fact, 412611 = 137537 × 3
550148: in fact, 550148 = 137537 × 4
687685: in fact, 687685 = 137537 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 137537, the answer is: yes, 137537 is a prime number because it only has two different divisors: 1 and itself (137537).
To know the primality of an integer, we can use several algorithms. The most naive is to try all divisors below the number you want to know if it is prime (in our case 137537). We can already eliminate even numbers bigger than 2 (then 4 , 6 , 8 ...). Besides, we can stop at the square root of the number in question (here 370.86 ). Historically, the Eratosthenes screen (which dates back to Antiquity) uses this technique relatively effectively.
More modern techniques include the Atkin screen, probabilistic tests, or the cyclotomic test.
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